Sloan, 68, has been the coach of the NBA team since December 1988.
The surprise development comes the morning after Sloan was involved in a long discussion behind closed doors with general manager Kevin O'Connor, following the Jazz's 91-86 loss to the Chicago Bulls, the Tribune said on its website (www.sltrib.com).
Sloan appeared visibly shaken after the meeting, and would not discuss what was said, the newspaper said.
The Hall of Fame coach had reached an agreement in principle earlier this month to coach the Jazz through the 2011-12 season.
Sloan, who also coached the Chicago Bulls, has a 1,221-803 career record. He is the only NBA coach to win 1,000 games with a single franchise.
The Jazz, 31-23 this season, would not confirm the report but said in a statement they will make a "significant announcement related to the team" at a 3 p.m. MST (2200 GMT) news conference on Thursday.
(Reporting by Gene Cherry in Salvo, North Carolina. Editing by Steve Ginsburg)